As an evidence of the durability of wooden teeth, there appeared in Engineering of January 7th, 1879, the illustration shown in [Fig. 182], which represents a cog from a wheel of 14 ft. 1⁄2 in. diameter, and having a 10-inch face, its pinion being 4 ft. in diameter. This cog had been running for 261⁄2 years, day and night; not a cog in the wheel having been touched during that time. Its average revolutions were 38 per minute, the power developed by the engine being from 90 to 100 indicated horse-power. The teeth were composed of beech, and had been greased twice a week, with tallow and plumbago ore.
Since the width of the face of a wheel influences its wear (by providing a larger area of contact over which the pressure may be distributed, as well as increasing the strength), two methods of proportioning the breadth may be adopted. First, it may be made a certain proportion of the pitch; and secondly, it may be proportioned to the pressure transmitted and the number of revolutions. The desirability of the second is manifest when we consider that each tooth will pass through the arcs of contact (and thus be subjected to wear) once during each revolution; hence, by making the number of revolutions an element in the calculation to find the breadth, the latter is more in proportion to the wear than it would be if proportioned to the pitch.
It is obvious that the breadth should be sufficient to afford the required degree of strength with a suitable factor of safety, and allowance for wear of the smallest wheel in the pair or set, as the case may be.
According to Reuleaux, the face of a wheel should never be less than that obtained by multiplying the gross pressure, transmitted in lbs., by the revolutions per minute, and dividing the product by 28,000.
In the case of bevel-wheels the pitch increases, as the perimeter of the wheel is approached, and the maximum pitch is usually taken as the designated pitch of the wheel. But the mean pitch is that which should be taken for the purposes of calculating the strength, it being in the middle of the tooth breadth. The mean pitch is also the diameter of the pitch circle, used for ascertaining the velocity of the wheel as an element in calculating the safe pressure, or the amount of power the wheel is capable of transmitting, and it is upon this basis that the values for bevel-wheels in the above table are computed.
In many cases it is required to find the amount of horse-power a wheel will transmit, or the proportions requisite for a wheel to transmit a given horse-power; and as an aid to the necessary calculations, the following table is given of the amount of horse-power that may be transmitted with safety, by the various wheels at the given velocities, with a wheel of an inch pitch and an inch face, from which that for other pitches and faces may be obtained by proportion.
TABLE SHOWING THE HORSE-POWER WHICH DIFFERENT
KINDS OF GEAR-WHEELS OF ONE INCH PITCH AND ONE
INCH FACE WILL SAFELY TRANSMIT AT VARIOUS
VELOCITIES OF PITCH CIRCLE.
| Velocity of Pitch Circle in Feet per Second. | Spur-Wheels. H.P. | Spur Mortise Wheels. H.P. | Bevel-Wheels. H.P. | Bevel Mortise Wheels. H.P. | ||||
| 2 | 1.3 | 38 | .6 | 47 | .9 | 38 | .6 | 47 |
| 3 | 1.7 | 56 | .9 | 71 | 1.2 | 27 | .8 | 56 |
| 6 | 2.7 | 82 | 1.7 | 6 | 1.7 | 6 | 1.3 | 63 |
| 12 | 4.4 | 3 | 3.1 | 3.1 | 2.1 | 6 | ||
| 18 | 5.7 | 93 | 4.0 | 58 | 4.0 | 58 | 2.8 | 47 |
| 24 | 7.0 | 25 | 4.9 | 31 | 4.9 | 31 | 3.4 | 47 |
| 30 | 8.1 | 82 | 5.7 | 27 | 5.7 | 27 | 4.0 | 36 |
| 36 | 9.1 | 63 | 6.4 | 14 | 6.4 | 14 | 4.5 | 16 |
| 42 | 10.1 | 56 | 7.1 | 02 | 7.1 | 02 | 4.9 | 63 |
| 48 | 11.0 | 83 | 7.6 | 80 | 7.6 | 80 | 5.4 | 11 |
In this table, as in the preceding one, the safe working pressure for 1-inch pitch and 1-inch breadth of face is supposed to be 400 lbs.
In cast gearing, the mould for which is made by a gear moulding machine, the element of draft to permit the extraction of the pattern is reduced: hence, the pressure of tooth upon tooth may be supposed to be along the full breadth of the tooth instead of at one corner only, as in the case of pattern-moulded teeth. But from the inaccuracies which may occur from unequal contraction in the cooling of the casting, and from possible warping of the casting while cooling, which is sure to occur to some extent, however small the amount may be, it is not to be presumed that the contact of the teeth of one wheel will be in all the teeth as perfect across the full breadth as in the case of machine-cut teeth. Furthermore, the clearance allowed for machine-moulded teeth, while considerably less than that allowed for pattern-moulded teeth, is greater than that allowed for machine-cut teeth; hence, the strength of machine-moulded teeth in proportion to the pitch lies somewhere between that of pattern-moulded and machine-cut teeth—but exactly where, it would be difficult to determine in the absence of experiments made for the purpose of ascertaining.